We present a measurement of the CP-violating asymmetry in B-0 ->rho(+)rho(-) decays using 535x10(6) B (B) over bar pairs collected with the Belle detector at the KEKB e(+)e(-) collider. We measure CP-violating coefficients A=0.16 +/- 0.21(stat)+/- 0.08(syst) and S=0.19 +/- 0.30(stat)+/- 0.08(syst). These values are used to determine the unitarity triangle angle phi(2) using an isospin analysis; the solution consistent with the standard model lies in the range 54 degrees <phi(2)< 113 degrees at the 90% confidence level.